Good Lord. He was hitting on the Danish PM something hard, in public, with his wife sitting right there next to him. This is about as close as sympathy for the wookie as I'm ever going to get, but what he did just isn't kosher. There's no holding of hands, but Obama's actions and the Wookie's scowl and body language make it crystal clear what he was doing.
The wookie may have cojones, but Obama's lucky she doesn't have those of Berlusconi's wife (he was the PM of Italy a while back), who demanded a public apology from him for his own similar behaviour, and got it from him in an open letter that was published.